We conducted a number of simulation studies to examine the asymptotic distribution of linear spectral statistics when the spectrums of \( \Sigma \)  are unbounded. In our experiments, we define \( {\bf Z}= \Sigma ^{\frac{1}{2}}{\bf X}\) , where \( {\bf X}=(x_{1},...,x_{n}) \) , and \( \left\lbrace x_{i} \right\rbrace _{1\le i\le n} \)  are \( p \) -variate random vectors, and we assume that they come from Gaussian distribution. Clearly, sample covariance matrix \( {\bf B}=\dfrac{1}{n}{\bf Z}{\bf Z}^{\prime } \) . Moreover, we set \( p=100 \) , \( n=3000 \) . About simulation we refer to [1]}, [2]}. For the setting of eigenvalues of \( \Sigma \) , we consider the following spectrums:
